Some Constacyclic Codes over Finite Chain Rings

TL;DR

This paper investigates the structure of constacyclic codes over finite chain rings, establishing their equivalence to cyclic codes under certain conditions and analyzing specific classes over Galois rings.

Contribution

It proves the equivalence of $\lambda$-constacyclic and cyclic codes over finite chain rings when $\lambda$ is an $n$-th power of a unit, simplifying their structure.

Findings

$\lambda$-constacyclic codes are equivalent to cyclic codes under certain conditions.

Simplified the structure of some constacyclic codes over finite chain rings.

Analyzed $\alpha + peta$-constacyclic codes over Galois rings.

Abstract

For $\lambda$ an $n$-th power of a unit in a finite chain ring we prove that $\lambda$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the $\alpha +p \beta$-constacyclic codes of length $p^s$ over the Galois ring $GR(p^e,r)$.